Analysis of runtime of optimization algorithms for noisy functions over discrete codomains

We consider in this work the application of optimization algorithms to problems over discrete codomains corrupted by additive unbiased noise. We propose a modification of the algorithms by repeating the fitness evaluation of the noisy function sufficiently so that, with a fix probability, the functi...

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Veröffentlicht in:Theoretical computer science Jg. 605; S. 42 - 50
Hauptverfasser: Akimoto, Youhei, Astete-Morales, Sandra, Teytaud, Olivier
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 09.11.2015
Elsevier
Schlagworte:
Additive noise
Algorithms
Discrete optimization
Fitness
Mathematical analysis
Mathematical models
Mathematics
Noise
Optimization
Optimization and Control
Resampling
Run time (computers)
Runtime analysis
Additive noise
Runtime analysis
Discrete optimization
Discrete Optimization
ISSN:0304-3975, 1879-2294
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Zusammenfassung:We consider in this work the application of optimization algorithms to problems over discrete codomains corrupted by additive unbiased noise. We propose a modification of the algorithms by repeating the fitness evaluation of the noisy function sufficiently so that, with a fix probability, the function evaluation on the noisy case is identical to the true value. If the runtime of the algorithms on the noise-free case is known, the number of resampling is chosen accordingly. If not, the number of resampling is chosen regarding to the number of fitness evaluations, in an anytime manner. We conclude that if the additive noise is Gaussian, then the runtime on the noisy case, for an adapted algorithm using resamplings, is similar to the runtime on the noise-free case: we incur only an extra logarithmic factor. If the noise is non-Gaussian but with finite variance, then the total runtime of the noisy case is quadratic in function of the runtime on the noise-free case.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2015.04.008